A person rows a boat in a water with a speed of `4 ms^(-1)`. Water in the river is flowing with a speed of `2 ms^(-1)` . If the person rows the boat perpendiculat to thedirection of flow, find resultant velcity of the boat and time taken by boat to cross the river if widthe of the river is `400 m`.

Explanation

Here, velocity of boat, ` v_b =4 ms^(-1)`
aling ` OB`
velocity of water, ` v_w =2 ms^(-1)` along (OA)`,
width of river ` =400 m, fig, 2 ( c ) .47.
.
` Resultant velocity of boat ` v_R` id along ` OC`. Then
` V_R = sqrt ( v_b ^2 = v_w ^2 ) = sqrt ( 4 ^2 + 2^20) = 4.472 m//s`
If ` vec(OC)` makes and angle ` thetga` with ` vec (OP)` then
` tan theta = v_w/v_b = 2/4 = 1/2 sin 30^@ or theta =30^@`
Time taken to cross the river,
` t= (4000)/v_b = ( 400)/4 = 100 s`.